Can my wife travel with a valid H4 visa stamped in old passport and she also got a new passport in which her name is corrected?

[sgj]

In her old passport her full name was printed in surname and given name was "blank". Recently we corrected the same by applying for a new passport. But the valid visa is in old passport. 

1. Will that be a problem for re-entry, if she travels with both passports? 
2. Do we need to work with HR to get the name change updated with USCIS before the travel? 

No change to employer or any other stuff. 

Experts, appreciate your thoughts on this. 

[xTDx]

21 hours ago, sgj said:

1. Will that be a problem for re-entry, if she travels with both passports? 
2. Do we need to work with HR to get the name change updated with USCIS before the travel? 

1. No issues.

2. No need , get it corrected while getting next amendment or extension os status.